He said the arguments put forward by Denis O'Brien and Dermot Desmond had 'no basis in Irish law'.

The judge said the key question was Mr McDowell's role with the tribunal.

He said Mr McDowell was not a part of the tribunal legal team and he accepted evidence from the tribunal that he had been retained as independent counsel to examine one witness.

Justice Hedigan accepted that this was quite a different role to the tribunal's full-time counsel who play a role in investigating matters.

A spokesman for Mr O'Brien and Mr Desmond said they intend to appeal the High Court decision.

Earlier this week, Denis O'Brien's lawyers told the court it was an unusual application and they recognised the right of the tribunal chairman to choose his own counsel.

However, they said the application was taken because of Mr McDowell's involvement in public affairs for the past 15 years.

Statements in the Dáil about the process of awarding a mobile phone licence to ESAT Digifone while he was a political opponent of Michael Lowry and his interaction with the tribunal while he was Attorney General all gave rise to concern about a potential conflict, they said.

The tribunal said the case being taken by the two businessmen simply 'did not get off the ground'.

They said allegations of bias could only be directed against a decision maker.

Mr McDowell was acting in a limited capacity for the tribunal and had no role of any kind in the decision-making process of the inquiry.